This invention relates to a video projection apparatus employing a lens such as a plastic lens whose focal length varies depending on the ambient temperature, and more particularly to an apparatus of the kind above described which is provided with a temperature compensation device capable of compensation of variations of the focal length of the lens due to temperature variations.
FIG. 1 shows the basic structure of a video projection apparatus. In FIG. 1, reference numerals 1, 2 and 3 designate a faceplate of a cathode-ray tube (CRT), a projection lens and a projection screen respectively. Although the lens 2 is usually a combination of a plurality of lenses, a single lens is illustrated in FIG. 1 as a representative of the combined lenses.
With the progress of the design and manufacturing technique of plastic lenses, a methacrylic resin having a high transparency and a light weight has become increasingly used in recent years as the material of plastic lenses.
Since the methacrylic resin has a refractive index variable depending on the ambient temperature, and, therefore, the focal length of a lens made of the methacrylic resin varies depending on the ambient temperature, such a lens when used as a projection lens has been defective in that the focus of a projected image tends to be degraded with variations of the ambient temperature.
FIG. 2 illustrates how the focal length of such a plastic lens increases with a temperature rise. In FIG. 2, the solid lines with arrows show the optical path at the room temperature, and the focal length of the lens 2 is f in that case:
At a higher temperature, the focal length f of the lens 2 increases by .DELTA.f as shown by the optical path represented by the dotted lines with arrows.
It is well known that the focal length f is given by the following expression (1): ##EQU2## where n: refractive index of lens medium (plastic), n.apprxeq.1.5.
R.sub.1, R.sub.2 : paraxial radii of curvature at planes of incidence and exit respectively of the lens.
It is known that the temperature dependence of the refractive index of the methacrylic resin is given by the following approximate expression (2) when the temperature T varies by .DELTA.T and the resultant variation of (n-1) is .DELTA.(n-1): ##EQU3## where PPM.tbd.10.sup.-6.
Since the coefficient of linear expansion of the methacrylic resin is about 80 PPM/.degree.C., the following approximate expression (3) is obtained: ##EQU4##
Substituting these values in the expression (1), the following approximate expression (4) is obtained: ##EQU5##
Suppose that a is the equivalent distance of the distance between the lens 2 and the faceplate 1 in FIG. 1 when calculated in terms of the distance in air, and b is the distance between the lens 2 and the projection screen 3. Then, ##EQU6##
The distance b remains constant regardless of temperature variations. Therefore, in order that the focus can be maintained to be unvariable regardless of variations of the focal length f of the lens 2, it is required that the equivalent distance a varies according to the following expression (6) obtained by substituting the expression (4) in the equation (5): ##EQU7## where M: magnification of projected image
In a projection television apparatus for home use, the value of M is commonly set at about 10. Therefore, substitution of M=10 in the expression (6) provides the following expression (7): ##EQU8##
Therefore, when the principal lens is subjected to a temperature rise of 20.degree. C. due to radiation of heat from the faceplate 1 of the CRT, the following relation is obtained: ##EQU9##
In order that the focus can be satisfactorily maintained to be unvariable, the equivalent distance a must be changed according to the expressions (6) to (8). However, realization of this requirement according to the prior art has been extremely difficult. Therefore, when the optical path is traced in the reverse direction from the projection screen 3 toward the CRT, a focus degradation as shown by d in FIG. 2 has occurred inevitably. There is the following relation between the diameter D of the lens 2 and the focus degradation d: ##EQU10##
In the case of the lens 2 having a low f-number and a large aperture used in the projection television apparatus, its diameter D is approximately equal to one-half the height of the image area of the phosphor screen of the faceplate 1 of the CRT, the value given by the equation (9) can be regarded to represent the degradation of the resolution of the projection television apparatus in terms of the number of scanning lines due to the temperature rise of the lens 2. It can be seen, by substitution of the value of the expression (8) in the equation (9), that a lens temperature rise of 20.degree. C. results in such a degradation of the resolution that the number of completely resolvable scanning lines is reduced to only about 140.
In view of the fact that a scene is displayed by 490 scanning lines on the screen of the CRT, such an excessive degradation of the resolution has been extremely insufficient for the complete reproduction of information.
In the prior art, a layer of a liquid is formed in a sandwich fashion on the faceplate of a CRT to be used as a coolant for the purpose of improving the adverse effect of radiation of heat from the CRT. The liquid layer can sufficiently serve the cooling purpose when it has a thickness of about 3 to 5 mm. However, the temperature compensation device according to the present invention differs distinctly from such a prior art device in its object and meritorious effects.